• Particle is at equilibrium if: – at rest – moving at a
constant velocity in a straight line
• Newton’s first law of motion! F = 0
– where ! F is the vector sum of all the forces acting on the
particle
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Free Body Diagram
• best representation of all the unknown forces ( ! F ) which
acts ona body
• a sketch showing the particle “free” from the surroundings
with allthe forces acting on it
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Free Body Diagram
Procedure:1. draw outlined shape
• isolate particle from its surroundings
2. show all the forces• indicate all the forces• active forces:
set the particle in motion• reactive forces: result of constraints
and supports that tend to
prevent motion
3. identify each force• known forces should be labeled with
proper magnitude and
direction• letters are used to represent magnitude and
directions of unknown
forces7
FBD Examples
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FBD Examples
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Coplanar Force Systems
• for a particle subjected to coplanar forces in the x- y plane
– resolve into i and j components – for equilibrium
! F x = 0 ! F y = 0
• Scalar equations of equilibrium – require the algebraic sum of
the
x and y components to equal zero – sense of direction =
algebraic sign corresponding to the arrowhead
direction
– for unknown magnitude, assume arrowhead sense of the force –
if the scalar is negative, the force is acting in the opposite
direction
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PF3-2
• The beam has a weight of 3.5kN. Determine the shortest cable
ABC that can be used to lift it if the maximum force the cable
cansustain is 7.5kN.
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P3-7
• The towing pendant AB is subjected to a force of 50kN
exertedby a tugboat. Determine the force in each of the bridles, BC
and BD, if the ship is moving forward with constant velocity.
